Ch.1 Properties
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| Definition of Subtraction | a - b = a + (-b)
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| Definition of Division | a ÷ b = a/b = a ∙ 1/b, b≠0
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| Distributive Property for Subtraction | a(b - c) = ab - ac
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| Multiplication by 0 | 0 ∙ a = -a
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| Multiplication by -1 | -1 ∙ a = -a
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| Opposite of a Sum | -(a + b) = -a + (-b)
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| Opposite of a Difference | -(a -b) = b-a
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| Opposite of a Product | -(ab) = -a ∙ b = a ∙(-b)
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| Opposite of an Opposite | -(-a) = a
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| Reflexive Property of Equality | a = a
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| Symmetric Property of Equality | If a = b, then b = a
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| Transitive Property of Equality | If a = b and b = c, then a = c
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| Addition Property of Equality | If a = b, then a + c = b + c
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| Subtraction Property of Equality | If a = b, then a - c = b - c
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| Multiplication Property of Equality | If a = b, then ac = bc
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| Division Property of Equality | If a = b and c ≠ 0, then a/c = b/c
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| Substitution Property of Equality | If a = b, then b may be substituted for a in any expression to obtain an equivalent expression
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| Transitive Property of Inequality | If a ≤ b and b ≤ c, then a ≤ c
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| Addition Property of Inequality | If a ≤ b, then a + c ≤ b + c
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| Subtraction Property of Inequality | If a ≤ b, then a - c ≤ b - c
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| Multiplication Property of Inequality | If a ≤ b and c > 0, then ac ≤ bc. If a ≤ b and c < 0, then ac ≥ bc.
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| Division Property of Inequality | If a ≤ b and c > 0, then a/c ≤ b/c. If a ≤ b and c < 0, then a/c ≥ b/c.
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| Closure of Addition | a + b is a real number
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| Closure of Multiplication | ab is a real number
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| Communtative of Addition | a + b = b + a
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| Communtative of Multiplication | ab = ba
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| Associative of Addition | (a + b) + c = a + (b +c)
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| Associative of Multiplication | (ab)c = a(bc)`
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| Identity of Addition | a + 0 = a, 0 + a = a
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| Identity of Multiplication | a ∙ 1 = a, 1∙ a = a
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| Inverse of Addition | a + (-a) = 0
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| Inverse of Multiplication | a ∙ 1/a = 1, a ≠ 0
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| Distributive | a(b + c) = ab + ac
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To hide a column, click on the column name.
To hide the entire table, click on the "Hide All" button.
You may also shuffle the rows of the table by clicking on the "Shuffle" button.
Or sort by any of the columns using the down arrow next to any column heading.
If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
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Created by:
gnomealot
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